# Extremal Depth for Functional Data and Applications

arXiv: https://arxiv.org/abs/1511.00128 · HTML: https://mlsanity.com/paper/1511.00128/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 Oct 2015.

## Built on by (most cited first, 5 of 5)

- [On projection methods for functional time series forecasting](https://mlsanity.com/paper/2105.04399/) (2021)
- [Data Depth and Core-based Trend Detection on Blockchain Transaction Networks](https://mlsanity.com/paper/2303.14241/) (2023)
- [Extreme Scenario Selection in Day-Ahead Power Grid Operational Planning](https://mlsanity.com/paper/2309.11067/) (2023)
- [Feature Selection using e-values](https://mlsanity.com/paper/2206.05391/) (2022)
- [Model-Free Kernel Conformal Depth Measures Algorithm for Uncertainty Quantification in Regression Models in Separable Hilbert Spaces](https://mlsanity.com/paper/2506.08325/) (2025)

## Abstract (arXiv)

We propose a new notion called `extremal depth' (ED) for functional data, discuss its properties, and compare its performance with existing concepts. The proposed notion is based on a measure of extreme `outlyingness'. ED has several desirable properties that are not shared by other notions and is especially well suited for obtaining central regions of functional data and function spaces. In particular: a) the central region achieves the nominal (desired) simultaneous coverage probability; b) there is a correspondence between ED-based (simultaneous) central regions and appropriate point-wise central regions; and c) the method is resistant to certain classes of functional outliers. The paper examines the performance of ED and compares it with other depth notions. Its usefulness is demonstrated through applications to constructing central regions, functional boxplots, outlier detection, and simultaneous confidence bands in regression problems.